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Simple quantum error-correcting codes

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Steane, A. M.·1996·Physical Review A

DOI 10.1103/physreva.54.4741

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Abstract

Methods of finding good quantum error-correcting codes are discussed, and many example codes are presented. The recipe ${\mathit{C}}_{2}^{\mathrm{\ensuremath{\perp}}}$\ensuremath{\subset}${\mathit{C}}_{1}$, where ${\mathit{C}}_{1}$ and ${\mathit{C}}_{2}$ are classical codes, is used to obtain codes for up to 16 information quantum bits (qubits) with correction of small numbers of errors. The results are tabulated. More efficient codes are obtained by allowing ${\mathit{C}}_{1}$ to have reduced distance, and introducing sign changes among the code words in a systematic manner. This systematic approach leads to single-error-correcting codes for 3, 4, and 5 information qubits with block lengths of 8, 10, and 11 qubits, respectively. \textcopyright{} 1996 The American Physical Society.

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The Theory of Error-Correcting Codes
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Self-citation
Good quantum error-correcting codes exist
Calderbank, A. R., & Shor, P. W. (1996) · Physical Review A · doi:10.1103/physreva.54.1098 · Cited by 2,516
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Self-citation
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Gottesman, D. (1996) · Physical Review A · doi:10.1103/physreva.54.1862 · Cited by 1,227 · cited 1×
“However, whereas the pioneering works just mentioned established the possibility of efficient quantum error correction, and presented the simplest codes possible, they did not address the more pragmatic issue of identifying other specific useful codes.”
Background
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Authors: Steane, A. M.
Affiliations: University of Oxford (GB)
Corresponding author: Steane, A. M.
ORCID: Steane, A. M.
Venue: Physical Review A
Publisher: American Physical Society (APS)
Published: 1996-12-01
Volume: 54
Issue: 6
Pages: 4741-4751
ISSN: 0556-2791 (ISSN-L)
1050-2947
1094-1622
DOI: 10.1103/physreva.54.4741
OpenAlex: W2063592138
Cited by: 522
References: 15
Citations by year: 2026: 28 · 2025: 50 · 2024: 34 · 2023: 37 · 2022: 37 · 2021: 21 · 2020: 37 · 2019: 20 · 2018: 17 · 2017: 12 · 2016: 15 · 2015: 17 · 2014: 14 · 2013: 14 · 2012: 11
FWCI: 16.25
Type: journal article
Language: en
Open access: green
arxiv.org
Licence: link.aps.org/licenses/aps-default-license (vor)
Locations: Physical Review A (publishedVersion)
PubMed (publishedVersion)
arXiv (Cornell University) (submittedVersion)
arXiv (Cornell University)
Funders: Royal Society
Topics: Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Coding theory and cryptography
Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
Keywords: quantum error-correcting codes, CSS construction, classical codes, qubits, single-error-correcting codes, code distance, systematic codes, block length, quantum information

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Simple quantum error-correcting codes

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